ON DISCRETE MEAN VALUES OF DIRICHLET L-FUNCTIONS

被引：1

作者：

Elma, Ertan ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, 200 Univ Ave West, Waterloo, ON N2L 3G1, Canada

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2021年 / 71卷 / 04期

关键词：

Dirichlet L-function; mean value; Dirichlet character;

D O I：

10.21136/CMJ.2021.0189-20

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let chi be a nonprincipal Dirichlet character modulo a prime number p >= 3 and let a(chi) := 1/2(1 - chi(-1)). Define the mean value M-p(-s, chi) := 2/p-1 Sigma L psi(modp)psi(-1)=-1(1, psi)L(-s, chi(psi) over bar)(sigma := Rs > 0). We give an identity for M-p(-s, chi) which, in particular, shows that M-p(-s, chi) = L(1-s, chi) + a(chi)2p(s)L(1, chi)zeta(-s) + o(1) (p -> infinity) for fixed 0 < sigma < 1/2 and vertical bar t := Js vertical bar = o(p((1-2 sigma)/(3+2 sigma))).

引用

页码：1035 / 1048

页数：14

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